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Identifier
Values
=>
0=>1 1=>1 00=>1 01=>1 10=>1 11=>1 000=>1 001=>1 010=>2 011=>1 100=>1 101=>2 110=>1 111=>1 0000=>1 0001=>1 0010=>2 0011=>1 0100=>2 0101=>3 0110=>2 0111=>1 1000=>1 1001=>2 1010=>3 1011=>2 1100=>1 1101=>2 1110=>1 1111=>1 00000=>1 00001=>1 00010=>2 00011=>1 00100=>3 00101=>3 00110=>2 00111=>1 01000=>2 01001=>4 01010=>6 01011=>3 01100=>2 01101=>4 01110=>2 01111=>1 10000=>1 10001=>2 10010=>4 10011=>2 10100=>3 10101=>6 10110=>4 10111=>2 11000=>1 11001=>2 11010=>3 11011=>3 11100=>1 11101=>2 11110=>1 11111=>1 000000=>1 000001=>1 000010=>2 000011=>1 000100=>3 000101=>3 000110=>2 000111=>1 001000=>3 001001=>5 001010=>7 001011=>3 001100=>3 001101=>4 001110=>2 001111=>1 010000=>2 010001=>4 010010=>8 010011=>4 010100=>7 010101=>11 010110=>7 010111=>3 011000=>2 011001=>5 011010=>7 011011=>5 011100=>2 011101=>4 011110=>2 011111=>1 100000=>1 100001=>2 100010=>4 100011=>2 100100=>5 100101=>7 100110=>5 100111=>2 101000=>3 101001=>7 101010=>11 101011=>7 101100=>4 101101=>8 101110=>4 101111=>2 110000=>1 110001=>2 110010=>4 110011=>3 110100=>3 110101=>7 110110=>5 110111=>3 111000=>1 111001=>2 111010=>3 111011=>3 111100=>1 111101=>2 111110=>1 111111=>1 0000000=>1 0000001=>1 0000010=>2 0000011=>1 0000100=>3 0000101=>3 0000110=>2 0000111=>1 0001000=>4 0001001=>5 0001010=>7 0001011=>3 0001100=>3 0001101=>4 0001110=>2 0001111=>1 0010000=>3 0010001=>6 0010010=>11 0010011=>5 0010100=>10 0010101=>13 0010110=>8 0010111=>3 0011000=>3 0011001=>7 0011010=>9 0011011=>5 0011100=>3 0011101=>4 0011110=>2 0011111=>1 0100000=>2 0100001=>4 0100010=>9 0100011=>4 0100100=>11 0100101=>15 0100110=>10 0100111=>4 0101000=>7 0101001=>16 0101010=>24 0101011=>13 0101100=>9 0101101=>15 0101110=>7 0101111=>3 0110000=>2 0110001=>5 0110010=>10 0110011=>7 0110100=>8 0110101=>16 0110110=>11 0110111=>5 0111000=>2 0111001=>5 0111010=>7 0111011=>6 0111100=>2 0111101=>4 0111110=>2 0111111=>1 1000000=>1 1000001=>2 1000010=>4 1000011=>2 1000100=>6 1000101=>7 1000110=>5 1000111=>2 1001000=>5 1001001=>11 1001010=>16 1001011=>8 1001100=>7 1001101=>10 1001110=>5 1001111=>2 1010000=>3 1010001=>7 1010010=>15 1010011=>9 1010100=>13 1010101=>24 1010110=>16 1010111=>7 1011000=>4 1011001=>10 1011010=>15 1011011=>11 1011100=>4 1011101=>9 1011110=>4 1011111=>2 1100000=>1 1100001=>2 1100010=>4 1100011=>3 1100100=>5 1100101=>9 1100110=>7 1100111=>3 1101000=>3 1101001=>8 1101010=>13 1101011=>10 1101100=>5 1101101=>11 1101110=>6 1101111=>3 1110000=>1 1110001=>2 1110010=>4 1110011=>3 1110100=>3 1110101=>7 1110110=>5 1110111=>4 1111000=>1 1111001=>2 1111010=>3 1111011=>3 1111100=>1 1111101=>2 1111110=>1 1111111=>1 00000000=>1 00000001=>1 00000010=>2 00000011=>1 00000100=>3 00000101=>3 00000110=>2 00000111=>1 00001000=>4 00001001=>5 00001010=>7 00001011=>3 00001100=>3 00001101=>4 00001110=>2 00001111=>1 00010000=>4 00010001=>7 00010010=>12 00010011=>5 00010100=>11 00010101=>13 00010110=>8 00010111=>3 00011000=>4 00011001=>7 00011010=>9 00011011=>5 00011100=>3 00011101=>4 00011110=>2 00011111=>1 00100000=>3 00100001=>6 00100010=>13 00100011=>6 00100100=>16 00100101=>20 00100110=>13 00100111=>5 00101000=>11 00101001=>22 00101010=>31 00101011=>15 00101100=>12 00101101=>17 00101110=>8 00101111=>3 00110000=>3 00110001=>8 00110010=>15 00110011=>9 00110100=>12 00110101=>20 00110110=>13 00110111=>5 00111000=>3 00111001=>7 00111010=>9 00111011=>6 00111100=>3 00111101=>4 00111110=>2 00111111=>1 01000000=>2 01000001=>4 01000010=>9 01000011=>4 01000100=>13 01000101=>16 01000110=>11 01000111=>4 01001000=>12 01001001=>24 01001010=>35 01001011=>17 01001100=>15 01001101=>21 01001110=>10 01001111=>4 01010000=>7 01010001=>17 01010010=>35 01010011=>20 01010100=>31 01010101=>51 01010110=>33 01010111=>13 01011000=>9 01011001=>23 01011010=>32 01011011=>20 01011100=>9 01011101=>16 01011110=>7 01011111=>3 01100000=>2 01100001=>5 01100010=>11 01100011=>7 01100100=>13 01100101=>23 01100110=>17 01100111=>7 01101000=>8 01101001=>21 01101010=>33 01101011=>22 01101100=>13 01101101=>24 01101110=>12 01101111=>5 01110000=>2 01110001=>5 01110010=>10 01110011=>8 01110100=>8 01110101=>17 01110110=>12 01110111=>7 01111000=>2 01111001=>5 01111010=>7 01111011=>6 01111100=>2 01111101=>4 01111110=>2 01111111=>1 10000000=>1 10000001=>2 10000010=>4 10000011=>2 10000100=>6 10000101=>7 10000110=>5 10000111=>2 10001000=>7 10001001=>12 10001010=>17 10001011=>8 10001100=>8 10001101=>10 10001110=>5 10001111=>2 10010000=>5 10010001=>12 10010010=>24 10010011=>13 10010100=>22 10010101=>33 10010110=>21 10010111=>8 10011000=>7 10011001=>17 10011010=>23 10011011=>13 10011100=>7 10011101=>11 10011110=>5 10011111=>2 10100000=>3 10100001=>7 10100010=>16 10100011=>9 10100100=>20 10100101=>32 10100110=>23 10100111=>9 10101000=>13 10101001=>33 10101010=>51 10101011=>31 10101100=>20 10101101=>35 10101110=>17 10101111=>7 10110000=>4 10110001=>10 10110010=>21 10110011=>15 10110100=>17 10110101=>35 10110110=>24 10110111=>12 10111000=>4 10111001=>11 10111010=>16 10111011=>13 10111100=>4 10111101=>9 10111110=>4 10111111=>2 11000000=>1 11000001=>2 11000010=>4 11000011=>3 11000100=>6 11000101=>9 11000110=>7 11000111=>3 11001000=>5 11001001=>13 11001010=>20 11001011=>12 11001100=>9 11001101=>15 11001110=>8 11001111=>3 11010000=>3 11010001=>8 11010010=>17 11010011=>12 11010100=>15 11010101=>31 11010110=>22 11010111=>11 11011000=>5 11011001=>13 11011010=>20 11011011=>16 11011100=>6 11011101=>13 11011110=>6 11011111=>3 11100000=>1 11100001=>2 11100010=>4 11100011=>3 11100100=>5 11100101=>9 11100110=>7 11100111=>4 11101000=>3 11101001=>8 11101010=>13 11101011=>11 11101100=>5 11101101=>12 11101110=>7 11101111=>4 11110000=>1 11110001=>2 11110010=>4 11110011=>3 11110100=>3 11110101=>7 11110110=>5 11110111=>4 11111000=>1 11111001=>2 11111010=>3 11111011=>3 11111100=>1 11111101=>2 11111110=>1 11111111=>1 000000000=>1 000000001=>1 000000010=>2 000000011=>1 000000100=>3 000000101=>3 000000110=>2 000000111=>1 000001000=>4 000001001=>5 000001010=>7 000001011=>3 000001100=>3 000001101=>4 000001110=>2 000001111=>1 000010000=>5 000010001=>7 000010010=>12 000010011=>5 000010100=>11 000010101=>13 000010110=>8 000010111=>3 000011000=>4 000011001=>7 000011010=>9 000011011=>5 000011100=>3 000011101=>4 000011110=>2 000011111=>1 000100000=>4 000100001=>8 000100010=>16 000100011=>7 000100100=>19 000100101=>22 000100110=>14 000100111=>5 000101000=>14 000101001=>24 000101010=>33 000101011=>15 000101100=>13 000101101=>17 000101110=>8 000101111=>3 000110000=>4 000110001=>10 000110010=>17 000110011=>9 000110100=>14 000110101=>20 000110110=>13 000110111=>5 000111000=>4 000111001=>7 000111010=>9 000111011=>6 000111100=>3 000111101=>4 000111110=>2 000111111=>1 001000000=>3 001000001=>6 001000010=>14 001000011=>6 001000100=>20 001000101=>24 001000110=>16 001000111=>6 001001000=>19 001001001=>35 001001010=>50 001001011=>23 001001100=>21 001001101=>28 001001110=>13 001001111=>5 001010000=>11 001010001=>27 001010010=>52 001010011=>27 001010100=>46 001010101=>67 001010110=>42 001010111=>15 001011000=>14 001011001=>31 001011010=>41 001011011=>23 001011100=>12 001011101=>18 001011110=>8 001011111=>3 001100000=>3 001100001=>8 001100010=>18 001100011=>11 001100100=>21 001100101=>34 001100110=>24 001100111=>9 001101000=>13 001101001=>32 001101010=>47 001101011=>27 001101100=>19 001101101=>29 001101110=>14 001101111=>5 001110000=>3 001110001=>8 001110010=>15 001110011=>11 001110100=>12 001110101=>22 001110110=>15 001110111=>7 001111000=>3 001111001=>7 001111010=>9 001111011=>6 001111100=>3 001111101=>4 001111110=>2 001111111=>1 010000000=>2 010000001=>4 010000010=>9 010000011=>4 010000100=>14 010000101=>16 010000110=>11 010000111=>4 010001000=>16 010001001=>28 010001010=>40 010001011=>18 010001100=>18 010001101=>23 010001110=>11 010001111=>4 010010000=>12 010010001=>29 010010010=>57 010010011=>29 010010100=>52 010010101=>75 010010110=>47 010010111=>17 010011000=>17 010011001=>38 010011010=>51 010011011=>28 010011100=>15 010011101=>23 010011110=>10 010011111=>4 010100000=>7 010100001=>17 010100010=>40 010100011=>22 010100100=>50 010100101=>77 010100110=>54 010100111=>20 010101000=>33 010101001=>80 010101010=>120 010101011=>67 010101100=>47 010101101=>75 010101110=>35 010101111=>13 010110000=>9 010110001=>25 010110010=>51 010110011=>34 010110100=>41 010110101=>77 010110110=>51 010110111=>22 010111000=>9 010111001=>25 010111010=>34 010111011=>24 010111100=>9 010111101=>16 010111110=>7 010111111=>3 011000000=>2 011000001=>5 011000010=>11 011000011=>7 011000100=>16 011000101=>25 011000110=>19 011000111=>7 011001000=>14 011001001=>35 011001010=>54 011001011=>31 011001100=>24 011001101=>38 011001110=>19 011001111=>7 011010000=>8 011010001=>22 011010010=>47 011010011=>32 011010100=>42 011010101=>80 011010110=>55 011010111=>24 011011000=>13 011011001=>35 011011010=>51 011011011=>35 011011100=>15 011011101=>28 011011110=>12 011011111=>5 011100000=>2 011100001=>5 011100010=>11 011100011=>8 011100100=>13 011100101=>25 011100110=>19 011100111=>10 011101000=>8 011101001=>22 011101010=>35 011101011=>27 011101100=>14 011101101=>29 011101110=>16 011101111=>7 011110000=>2 011110001=>5 011110010=>10 011110011=>8 011110100=>8 011110101=>17 011110110=>12 011110111=>8 011111000=>2 011111001=>5 011111010=>7 011111011=>6 011111100=>2 011111101=>4 011111110=>2 011111111=>1 100000000=>1 100000001=>2 100000010=>4 100000011=>2 100000100=>6 100000101=>7 100000110=>5 100000111=>2 100001000=>8 100001001=>12 100001010=>17 100001011=>8 100001100=>8 100001101=>10 100001110=>5 100001111=>2 100010000=>7 100010001=>16 100010010=>29 100010011=>14 100010100=>27 100010101=>35 100010110=>22 100010111=>8 100011000=>10 100011001=>19 100011010=>25 100011011=>13 100011100=>8 100011101=>11 100011110=>5 100011111=>2 100100000=>5 100100001=>12 100100010=>28 100100011=>15 100100100=>35 100100101=>51 100100110=>35 100100111=>13 100101000=>24 100101001=>55 100101010=>80 100101011=>42 100101100=>32 100101101=>47 100101110=>22 100101111=>8 100110000=>7 100110001=>19 100110010=>38 100110011=>24 100110100=>31 100110101=>54 100110110=>35 100110111=>14 100111000=>7 100111001=>19 100111010=>25 100111011=>16 100111100=>7 100111101=>11 100111110=>5 100111111=>2 101000000=>3 101000001=>7 101000010=>16 101000011=>9 101000100=>24 101000101=>34 101000110=>25 101000111=>9 101001000=>22 101001001=>51 101001010=>77 101001011=>41 101001100=>34 101001101=>51 101001110=>25 101001111=>9 101010000=>13 101010001=>35 101010010=>75 101010011=>47 101010100=>67 101010101=>120 101010110=>80 101010111=>33 101011000=>20 101011001=>54 101011010=>77 101011011=>50 101011100=>22 101011101=>40 101011110=>17 101011111=>7 101100000=>4 101100001=>10 101100010=>23 101100011=>15 101100100=>28 101100101=>51 101100110=>38 101100111=>17 101101000=>17 101101001=>47 101101010=>75 101101011=>52 101101100=>29 101101101=>57 101101110=>29 101101111=>12 101110000=>4 101110001=>11 101110010=>23 101110011=>18 101110100=>18 101110101=>40 101110110=>28 101110111=>16 101111000=>4 101111001=>11 101111010=>16 101111011=>14 101111100=>4 101111101=>9 101111110=>4 101111111=>2 110000000=>1 110000001=>2 110000010=>4 110000011=>3 110000100=>6 110000101=>9 110000110=>7 110000111=>3 110001000=>7 110001001=>15 110001010=>22 110001011=>12 110001100=>11 110001101=>15 110001110=>8 110001111=>3 110010000=>5 110010001=>14 110010010=>29 110010011=>19 110010100=>27 110010101=>47 110010110=>32 110010111=>13 110011000=>9 110011001=>24 110011010=>34 110011011=>21 110011100=>11 110011101=>18 110011110=>8 110011111=>3 110100000=>3 110100001=>8 110100010=>18 110100011=>12 110100100=>23 110100101=>41 110100110=>31 110100111=>14 110101000=>15 110101001=>42 110101010=>67 110101011=>46 110101100=>27 110101101=>52 110101110=>27 110101111=>11 110110000=>5 110110001=>13 110110010=>28 110110011=>21 110110100=>23 110110101=>50 110110110=>35 110110111=>19 110111000=>6 110111001=>16 110111010=>24 110111011=>20 110111100=>6 110111101=>14 110111110=>6 110111111=>3 111000000=>1 111000001=>2 111000010=>4 111000011=>3 111000100=>6 111000101=>9 111000110=>7 111000111=>4 111001000=>5 111001001=>13 111001010=>20 111001011=>14 111001100=>9 111001101=>17 111001110=>10 111001111=>4 111010000=>3 111010001=>8 111010010=>17 111010011=>13 111010100=>15 111010101=>33 111010110=>24 111010111=>14 111011000=>5 111011001=>14 111011010=>22 111011011=>19 111011100=>7 111011101=>16 111011110=>8 111011111=>4 111100000=>1 111100001=>2 111100010=>4 111100011=>3 111100100=>5 111100101=>9 111100110=>7 111100111=>4 111101000=>3 111101001=>8 111101010=>13 111101011=>11 111101100=>5 111101101=>12 111101110=>7 111101111=>5 111110000=>1 111110001=>2 111110010=>4 111110011=>3 111110100=>3 111110101=>7 111110110=>5 111110111=>4 111111000=>1 111111001=>2 111111010=>3 111111011=>3 111111100=>1 111111101=>2 111111110=>1 111111111=>1 0000000001=>1 0010000001=>6 0010101101=>96 0010101011=>87 0010100111=>27 0010011101=>30 0010011011=>37 0010010111=>23 0010001111=>6 0001110101=>22 0001110011=>11 0001101101=>29 0001101011=>27 0001100111=>9 0001011101=>18 0001011011=>23 0001010111=>15 0001001111=>5 0000111101=>4 0000111011=>6 0000110111=>5 0000101111=>3 0000011111=>1 0000000000=>1 0000000110=>2 0000011000=>4 0000011110=>2 0000010010=>12 0001100000=>4 0001100110=>26 0001111000=>4 0001111110=>2 0001110010=>17 0001001000=>24 0001001110=>14 0001000010=>18 0001011010=>43 0010101010=>169 0010101000=>53 0010101100=>67 0010100100=>78 0010010100=>78 0001010100=>53 0010101110=>44 0010100000=>11 0010000100=>22 0000010100=>11 0000000010=>2 0000001110=>2 0000111110=>2 0000000100=>3 0000001010=>7 0000010110=>8 0000101110=>8 0001011110=>8 0001101110=>14 0001110110=>15 0001111010=>9 0001111100=>3 0000000101=>3 0000001101=>4 0000011101=>4 0001111101=>4 0000001001=>5 0000010101=>13 0000101101=>17 0010110001=>39 0001100001=>11 0001000001=>8 0000111111=>1 0001110100=>14 0001101100=>21 0010011100=>21 0001011100=>13 0000111100=>3 0001101010=>51 0010011010=>71 0000111010=>9 0010100110=>77 0010010110=>66 0001010110=>44 0000110110=>13 0010001110=>16 0001101001=>36 0000110001=>10 0000010001=>7 0000001100=>3 0000011001=>7 0000110011=>9 0000110100=>14 0000000011=>1 0000011011=>5 0001101111=>5 0000110101=>20 0010000010=>14 0001000011=>8 0010011110=>13 0001010000=>15 0001000100=>25 0001010101=>71 0001001011=>25 0001100011=>13 0001110111=>7 0010000000=>3 0000000111=>1 0000001111=>1 0001111111=>1 0000001011=>3 0000010111=>3 0001011111=>3 0001111001=>7 0000011010=>9 0000101010=>33 0000100101=>22 0010010001=>45 0010000101=>25 0010010101=>107 0010010011=>42 0000101011=>15 0001000111=>7 0000100111=>5 0010010010=>86 0001001010=>57 0001001001=>41 0001000101=>29 0000100011=>7 0000100100=>20 0000100010=>17 0010110000=>14 0000011100=>3 0000001000=>4 0000101100=>13 0010101111=>15 0000101000=>15 0010001000=>25 0001001100=>24 0001000110=>19 0001100100=>26 0001100010=>23 0000100110=>14 0000110010=>17 0010010000=>20 0001010010=>60 0001000000=>4 0001011001=>33 0001100101=>38 0001110001=>10 0010011001=>54 0010100101=>113 0010101001=>117 0010011111=>5 0000111001=>7 0010001101=>34 0001001101=>30 0001010001=>33 0001010011=>29 0001111011=>6 0010011000=>26 0001011000=>17 0000100000=>5 0010001011=>27 0010000111=>6 0000010011=>5 0010001100=>27 0010000110=>17 0000110000=>5 0000100001=>9 0010100011=>34 0010100001=>28 0000111000=>4 0001101000=>17 0000010000=>5 0000101001=>24 0010100010=>64 0010001001=>43 0010000011=>6 0010001010=>61 0001110000=>4
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Description
The number of standard Young tableaux whose descent set is the binary word.
A descent in a standard Young tableau is an entry $i$ such that $i+1$ appears in a lower row in English notation.
For example, the tableaux $[[1,2,4],[3]]$ and $[[1,2],[3,4]]$ are those with descent set $\{2\}$, corresponding to the binary word $010$.
Code
def statistic(w):
    D = [i+1 for i in range(len(w)) if w[i]==1]
    return len([T for T in StandardTableaux(len(w)+1)
                if T.standard_descents() == D])

Created
Jun 15, 2017 at 08:07 by Martin Rubey
Updated
Jun 15, 2017 at 08:07 by Martin Rubey